MinT - Best Known (250−140, 250, s)-Nets in Base 3

Best Known (250−140, 250, s)-Nets in Base 3

(250−140, 250, 74)-Net over F₃ — Constructive and digital

Digital (110, 250, 74)-net over F₃, using

t-expansion [i] based on digital (107, 250, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(250−140, 250, 104)-Net over F₃ — Digital

Digital (110, 250, 104)-net over F₃, using

t-expansion [i] based on digital (102, 250, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(250−140, 250, 613)-Net in Base 3 — Upper bound on s

There is no (110, 250, 614)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199806 531181 778554 958710 562795 308251 571625 289203 930687 155302 679532 816047 590220 071606 907533 753876 910104 883365 837591 612309 > 3²⁵⁰ [i]